[R] Sampling of non-overlapping intervals of variable length

[Charles C. Berry]

On Sun, 19 Jul 2009, Hadassa Brunschwig wrote:

> Hi
>
> I am not sure what you mean by sampling an index of a group of
> intervals. I will try to give an example:
> Let's assume I have a vector 1:1000000. Let's say I have 10 intervals
> of different but known length, say,
> c(4,6,11,2,8,14,7,2,18,32). For simulation purposes I have to sample
> those 10 intervals 1000 times.
> The requirement is, however, that they should be of those lengths and
> should not be overlapping.
> In short, I would like to obtain a 10x1000 matrix with sampled intervals.

Something like this:


> lens <- c(4,6,11,2,8,14,7,2,18,32)
> perm.lens <- sample(lens)
> sort(sample(1e06-sum(lens)+length(lens),length(lens)))+cumsum(c(0,head(perm.lens,-1)))
  [1]  15424 261927 430276 445976 451069 546578 656123 890494 939714 969643
>

The vector above gives the starting points for the intervals whose lengths 
are perm.lens.

I'd bet every introductory combinatorics book has a problem or example in 
which the expression for the number of ways in which K ordered objects can 
be assigned to I groups consisting of n_i adjacent objects each is 
constructed. The construction is along the lines of the calculation above.

HTH,

Chuck


>
> Thanks
> Hadassa
>
> On Sun, Jul 19, 2009 at 9:48 PM, David Winsemius<dwinsemius at comcast.net> wrote:
>>
>> On Jul 19, 2009, at 1:05 PM, Hadassa Brunschwig wrote:
>>
>>> Hi,
>>>
>>> I hope I am not repeating a question which has been posed already.
>>> I am trying to do the following in the most efficient way:
>>> I would like to sample from a finite (large) set of integers n
>>> non-overlapping
>>> intervals, where each interval i has a different, set length L_i
>>> (which is the number
>>> of integers in the interval).
>>> I had the idea to sample recursively on a vector with the already
>>> chosen intervals
>>> discarded but that seems to be too complicated.
>>
>> It might be ridiculously easy if you sampled on an index of a group of
>> intervals.
>> Why not pose the question in the form of example data.frames or other
>> classes of R objects? Specification of the desired output would be
>> essential. I think further specification of the sampling strategy would also
>> help because I am unable to understand what sort of probability model you
>> are hoping to apply.
>>
>>> Any suggestions on that?
>>>
>>> Thanks a lot.
>>>
>>> Hadassa
>>>
>>>
>>> --
>>> Hadassa Brunschwig
>>> PhD Student
>>> Department of Statistics
>>
>>
>> David Winsemius, MD
>> Heritage Laboratories
>> West Hartford, CT
>>
>>
>
>
>
> -- 
> Hadassa Brunschwig
> PhD Student
> Department of Statistics
> The Hebrew University of Jerusalem
> http://www.stat.huji.ac.il
>
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>

Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901